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Like the discrete-time Markov decision processes, in continuous-time Markov decision processes the agent aims at finding the optimal policy which could maximize the expected cumulated reward. The only difference with the standard case stays in the fact that, due to the continuous nature of the time variable, the sum is replaced by an integral:
A partially observable Markov decision process (POMDP) is a Markov decision process in which the state of the system is only partially observed. POMDPs are known to be NP complete , but recent approximation techniques have made them useful for a variety of applications, such as controlling simple agents or robots.
A process with this property is said to be Markov or Markovian and known as a Markov process. Two famous classes of Markov process are the Markov chain and Brownian motion. Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition. Namely that the statespace of ...
A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state.
In probability theory, a Markov reward model or Markov reward process is a stochastic process which extends either a Markov chain or continuous-time Markov chain by adding a reward rate to each state. An additional variable records the reward accumulated up to the current time. [1]
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
A simple example is the strategy which selects ... This may be explained, at least in part, by the cost of evaluating candidates. ... A Markov decision process ...
Usually the term "Markov chain" is reserved for a process with a discrete set of times, that is, a discrete-time Markov chain (DTMC), [11] but a few authors use the term "Markov process" to refer to a continuous-time Markov chain (CTMC) without explicit mention.